London — Britain would extend an Australian-style points-based immigration system to European Union citizens if it votes to leave the bloc, the "Out" campaign said on Wednesday, ratcheting up the pressure on a key issue ahead of the June 23 referendum.

Two polls on Tuesday showed voters have moved towards backing Brexit after official figures last week put net migration in 2015 at the second highest level on record.

"Migration brings many benefits to Britain - culturally, socially and economically," they said in a joint statement.

"We want Britain to continue to benefit from migration. But if we are to welcome more people to Britain then the public must be reassured that we have control over who comes here. Our membership of the EU means we don't have control."

Prime Minister David Cameron, who supports an "In" vote, has come under fire for failing to deliver a 2010 promise to keep net migration to the "tens of thousands."

Last week's figures put net migration at 330,000 in 2015. Of those, a net 184,000 came from the EU.

Cameron told BBC Radio on Wednesday that if Britain were to require EU citizens get work permits to come to the country, European countries would set up reciprocal arrangements.

"So not only would we trash our economy, we'd also reduce opportunities for people to work in other countries," he said.

Immigration is one of the key battlegrounds in what is becoming an increasingly bitter debate ahead of Britain's EU vote. Supporters of EU membership have complained the Out campaign has failed to offer any concrete proposals as to what life would look like if Britain left the bloc.

Setting out its plans, the Out campaign said there would be no change for Irish citizens, who can live and work in Britain, while those EU citizens already lawfully resident in Britain could remain and be granted indefinite leave.

But by the next national election in 2020, the Out campaign said it would have extended a points-based system where EU citizens would be treated like any other and admitted on the basis of their suitability for a job.

While neither Johnson nor Gove have the power to implement the proposed changes, both are seen as potential successors to Cameron, who does not plan to seek a third term and would be under pressure to quit sooner after a vote for Brexit.

Business group the Confederation of British Industry said applying a points system to European citizens would mean giving up access to the single market, which it said would be "hugely damaging" to Britain's economy.